Oscillation analysis of solutions of non-zero continuous linear functional equations

Article type: Research Article

Authors: Yin, Nan

Affiliations: Business School, Nanjing Xiaozhuang University, Nanjing, Jiangsu 211171, China | E-mail: [email protected]

Correspondence: [*] Corresponding author: Business School, Nanjing Xiaozhuang University, Nanjing, Jiangsu 211171, China. E-mail: [email protected].

Abstract: As a mathematical model of mechanical and electronic oscillation, the study and analysis of the oscillation characteristics of the solution of the non-zero continuous linear functional equation are of great significance in theory and practice. In view of the oscillation characteristics of the solutions of the second and third order non-zero continuous functional equations, this paper puts forward a hypothesis, studies the oscillation and asymptotics of the non-zero continuous linear functional differential equations by using the generalized Riccati transformation and the integral average technique, and establishes some new sufficient conditions for the oscillation or convergence to zero of all solutions of the equations, so as to obtain a new theorem for the solutions of the non-zero continuous linear functional equations.

Keywords: Non-zero, continuous, linear, functional equation, oscillation, characteristic

DOI: 10.3233/JCM-215171

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 21, no. 3, pp. 763-773, 2021